Solve For X if archtan(x)+archsin(x)=3/4pi

Answer 1

I assume you mean

arctan(x)+arcsin(x)=3/4 π

well, you know that
π/4 + π/2 = 3/4 π
so, x=1

the hard way:

sin(arctan(x)+arcsin(x)) = 1/√2
sin(arctan(x))cos(arcsin(x)) + cos(arctan(x))sin(arcsin(x)) = 1/√2

Now draw the right triangles for arctan(x) and arcsin(x). Then you have

x/√(1+x^2) * √(1-x^2) + 1/√(1+x^2) * x = 1/√2

x√(1-x^2) + x = √(1+x^2)/√2
. . .

it is clear that x=1 satisfies this equation.